Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature

2024/01/07 by Qi Ding, Ding, Qi
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.03394

openalex publication_date 2024/01/07 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28

Abstract

Let Σ be a complete Riemannian manifold of nonnegative Ricci curvature. We prove a Liouville-type theorem: every smooth solution u to minimal hypersurface equation on Σ is a constant provided u has sublinear growth for its negative part. Here, the sublinear growth condition is sharp. Our proof relies on a gradient estimate for minimal graphs over Σ with small linear growth of the negative parts of graphic functions via iteration.

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